Bb2 in Werckmeister V
In Werckmeister V, Bb2 is tuned to 116.804 Hz (+3.90 cents from equal temperament). The surrounding chromatic notes at octave 2 are tuned according to a circulating temperament with only two narrowed fifths, producing the most equal key distribution of the Werckmeister family and approaching equal temperament.
This system was used for Scholarly temperament study and Baroque keyboard music requiring near-equal treatment.
Chromatic Scale at Octave 2 in Werckmeister V
The table below shows all 12 chromatic notes at octave 2 in Werckmeister V. Frequencies use A=440 Hz as the concert pitch reference.
| Note | Equal Temp (Hz) | Werckmeister V (Hz) | Deviation (cents) |
|---|---|---|---|
| C2 | 65.406 | 65.629 | +5.89 |
| Db2 | 69.296 | 69.374 | +1.95 |
| D2 | 73.416 | 73.749 | +7.83 |
| Eb2 | 77.782 | 77.958 | +3.91 |
| E2 | 82.407 | 82.314 | -1.95 |
| F2 | 87.307 | 87.504 | +3.90 |
| Gb2 | 92.499 | 92.499 | 0.00 |
| G2 | 97.999 | 98.443 | +7.83 |
| Ab2 | 103.826 | 103.709 | -1.95 |
| A2 | 110.000 | 110.000 | 0.00 |
| Bb2 | 116.541 | 116.804 | +3.90 |
| B2 | 123.471 | 123.611 | +1.96 |
Positive cents = sharper than equal temperament. Negative = flatter. 100 cents = 1 semitone.
Werckmeister V: Mathematical Formula
Werckmeister V narrows only two fifths — a minimal adjustment compared to Werckmeister III's four narrowed fifths and Werckmeister IV's complex mixed adjustments. The two narrowed fifths each lose approximately half the syntonic comma, while the remaining ten fifths are either pure or very close to pure. The result is a remarkably even distribution of key quality: no key is far from equal temperament, and the differences between near and remote keys are subtle. The major third on C is only slightly purer than in equal temperament, while major thirds in all other keys remain within a few cents. The system prioritizes fifths purity throughout.
Formula type: Cent offsets from equal temperament
How Werckmeister V Sounds
Werckmeister V sounds closer to equal temperament than any other Werckmeister variant. Key colors are subtle — present to a trained ear in sustained chords but not immediately obvious in melodic or rapid-tempo passages. The system has an evenness and neutrality that makes it suitable for music that ranges freely across many key centers. Compared to Werckmeister III, the contrast between a good key like C major and a remote key like F# major is reduced to a gentle shading rather than a dramatic shift in affect. This quality makes Werckmeister V somewhat unusual among historical temperaments in approaching the egalitarianism of equal temperament.
Historical Context
Werckmeister V appears in Andreas Werckmeister's 1691 treatise as an alternative for situations where nearly equal key quality was desirable. In practice, it was rarely adopted by historical keyboard players, who generally preferred the more colorful contrasts of Werckmeister III or IV. The temperament is primarily of scholarly interest today: it demonstrates the logical endpoint of the Werckmeister project — a system that solves the meantone wolf completely and distributes key quality nearly equally. Modern musicologists study it as a milestone in the theoretical development of equal temperament, which it anticipates without fully achieving.
Other Tuning Systems for Bb2
For a full deep dive into Werckmeister V, see the Tunable guide to Werckmeister V.
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